Spieth and Palmer fired a 6-under-par 66 in a foursomes (alternate shot) opening round at TPC Louisiana, a score matched by Kyle Stanley and Ryan Ruffels, an 18-year-old, Florida-born Australian.
The event is the first in the PGA Tour regular season to feature a team format since 1981.
"It looks like wind might pick up tomorrow afternoon, you never know," Spieth said. "But alternate-shot format with these conditions, anything 3 under or so was a solid score. Grab a few extra and be in obviously pole position, it's fantastic.
"We're just going to try and have as much fun as we had today. We really did. We were laughing a lot. ... We'll get out there tomorrow and try to get as many putts as we can ... in the wind."
Ruffels said, "I thought I hit it well until I saw Kyle start hitting the ball. That was pretty impressive. He hit a lot down the pin. I've been putting very well lately, so he gave me a lot of opportunities, and I was able to roll some in, and I struck it quite well, as well.
"Yeah, we just combined really well. He told me a couple days ago when we played on Tuesday, 'Let's try and play boring golf,' and for the most part that's what we did. We hit a lot of greens and we were able to roll a few in."
Four teams are tied for third at 67: the All-American duos of Ben Martin-Ben Crane and Charley Hoffman-Nick Watney, the South Korean pair of K.J. Choi and Charlie Wi, and the tandem of Sweden's Jonas Blixt and Australia's Cameron Smith.
Tied for seventh are four all-American pairs: Steve Stricker-Jerry Kelly, Brian Stuard-Chris Stroud, Patrick Reed-Patrick Cantlay and Xander Schauffele-Tag Ridings. The group features some veterans as Kelly and Stricker are each 50, Choi is 46, and Wi is 45.
The teams will play better ball Friday before the 36-hole cut is made.
The top 35 pairs will play another round of alternate shot Saturday and better ball Sunday to determine the champion.